In a small bowl, lightly whisk the egg, egg yolk and vanilla together. On low speed, gradually add the egg mixture and the milk mixture to the flour. Beat until combined. Switch to the dough hook. On medium speed, add the butter a little at a time, making sure each addition is incorporated before adding the next. Knead with the mixter until the dough is smooth and elastic, about 8-10 minutes. To determine if the dough is ready, pinch off a small piece of dough. It should stretch easily without tearing and look translucent.